The Contents pane is our primary interface for seeing the coordinate systems assigned to components and to edit those coordinate systems.
In Manifold, the terms "projection" and "coordinate system" are synonyms and are used interchangeably.
Manually assign the initial coordinate system when importing from a format that does not specify the coordinate system. 

Repair an incorrectly assigned initial coordinate system. Used when a mistake has been made with the Assign Initial Coordinate System command or when importing data from a format that specifies the initial coordinate system but which specifies the wrong coordinate system. 

Routine command to reproject data from one coordinate system into a different coordinate system. 

How projections for maps are specified. Maps can have a different projection than the native projection of the layers they include. 

A synonym for projection. Coordinate systems are an organized way to use numbers to specify locations. 

A subdialog of the Coordinate System dialog used to specify what is often called the ellipsoid or datum. 

Saved favorite base coordinate systems. Provides a oneclick, simplified way of specifying a frequently used base coordinate system. 

Saved favorite coordinate systems. Provides a oneclick, simplified way of specifying a frequently used coordinate system. 
Example: Assign Initial Coordinate System  Use the Contents pane to manually assign an initial coordinate system when importing from a format that does not specify the coordinate system.
Example: Change Projection of an Image  Use the Change Coordinate System command to change the projection of an image, raster data showing terrain elevations in a region of Florida, from Latitude / Longitude to Orthographic centered on Florida.